exactyoudaoicibaDictYouDict[exact 词源字典]
exact: [15] The adjective exact ‘precise’ and the verb exact ‘demand with severity’ have undergone considerable semantic divergence over the centuries, but they both go back to the same source, the Latin verb exigere (from which English also got essay, examine, exigent [15], and exiguous [17]). This, a compound of the prefix ex- ‘out’ and agere ‘lead, drive’ (source of English act and agent), meant originally ‘drive out’, but in due course it developed the metaphorical senses ‘demand’ (preserved in the English verb), ‘weigh accurately’, and ‘bring to completion or perfection’.

These last two were taken up adjectivally in the Latin past participle exactus, from which English gets exact.
=> act, agent, essay, examine[exact etymology, exact origin, 英语词源]
exact (adj.)youdaoicibaDictYouDict
"precise, rigorous, accurate," 1530s, from Latin exactus "precise, accurate, highly finished," past participle adjective from exigere "demand, require, enforce," literally "to drive or force out," also "finish, measure," from ex- "out" (see ex-) + agere "drive, lead, act" (see act (n.)).
exact (v.)youdaoicibaDictYouDict
mid-15c., from Latin exactus, past participle of exigere "require, enforce, demand, collect (money);" see exact (adj.). Older in English than the adjective and retaining the literal sense of the Latin source. Related: Exacted; exacting.